Large-scale density and velocity field reconstructions with neural networks

We assess a neural network (NN) method for reconstructing 3D cosmological density and velocity fields (target) from discrete and incomplete galaxy distributions (input). We employ second-order Lagrangian Perturbation Theory to generate a large ensemble of mock data to train an autoencoder (AE) architecture with a Mean Squared Error (MSE) loss function. The AE successfully captures nonlinear features arising from gravitational dynamics {and} the discreteness of the galaxy distribution. In comparison, the traditional Wiener filter (WF) reconstruction exhibits a stronger suppression of the power on smaller scales and contains regions of unphysical negative densities. In the density reconstruction, the reduction of the AE MSE relative to the WF is $\sim 15 \%$, whereas for the velocity reconstruction a relative reduction of up to a factor of two can be achieved. The AE is particularly superior to the WF towards the tails of the density and velocity distributions. In fact, trained with an MSE loss, any NN estimate approaches the unbiased mean of the underlying target given the input. This implies a slope of unity in the linear regression of the true on the NN-reconstructed field. Only for the special case of Gaussian fields, the NN and WF estimates are equivalent. Nonetheless, we also recover a linear regression slope of unity for the WF with non-Gaussian fields.Comment: 17 pages, 13 figures. Submitted to MNRAS. Comments are welcom